Bubbling and hydra effect in a population system with Allee effect

IF 3.1 3区环境科学与生态学 Q2 ECOLOGY Ecological Complexity Pub Date : 2021-09-01 DOI:10.1016/j.ecocom.2021.100939

Koushik Garain , Partha Sarathi Mandal

引用次数: 8

Abstract

We present a continuous time predator-prey model and predator’s growth subjected to component Allee effect. The model also includes density dependent mortality of predator. We investigate our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect. In our system, we find that a fixed point representing the extinction of predator is always a stable point. When coexistence equilibria exists our system is bistable. We have observed that tristability is possible for our model that includes two stable co-existence fixed point. The most important phenomena which we have observed are hydra effect and cascading effect. Due to component Allee effect in predator the system shows multiple hydra effect. We discuss the phenomenon of bubbling, which indicates increasing and decreasing of amplitudes of cycles. We have presented one-parametric as well as two-parametric bifurcation diagram and also all possible bifurcations that the system could go through.

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具有Allee效应的种群系统中的气泡和水螅效应

我们提出了一个连续时间捕食者-被捕食者模型，以及受分量Allee效应影响的捕食者的生长。该模型还考虑了捕食者的密度依赖性死亡率。我们对我们的模型进行了分析和数值研究，并强调了密度无关死亡率和Allee效应的影响。在我们的系统中，我们发现一个表示捕食者灭绝的不动点总是一个稳定点。当共存平衡存在时，系统是双稳态的。我们已经观察到包含两个稳定共存不动点的模型是可能的三稳定性。我们观察到的最重要的现象是水螅效应和级联效应。由于捕食者中存在分量折线效应，系统呈现多重水螅效应。我们讨论了鼓泡现象，它表示周期振幅的增减。我们给出了单参数分岔图和双参数分岔图以及系统可能经历的所有可能的分岔图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ecological Complexity 环境科学-生态学

CiteScore

7.10

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： Ecological Complexity is an international journal devoted to the publication of high quality, peer-reviewed articles on all aspects of biocomplexity in the environment, theoretical ecology, and special issues on topics of current interest. The scope of the journal is wide and interdisciplinary with an integrated and quantitative approach. The journal particularly encourages submission of papers that integrate natural and social processes at appropriately broad spatio-temporal scales. Ecological Complexity will publish research into the following areas: • All aspects of biocomplexity in the environment and theoretical ecology • Ecosystems and biospheres as complex adaptive systems • Self-organization of spatially extended ecosystems • Emergent properties and structures of complex ecosystems • Ecological pattern formation in space and time • The role of biophysical constraints and evolutionary attractors on species assemblages • Ecological scaling (scale invariance, scale covariance and across scale dynamics), allometry, and hierarchy theory • Ecological topology and networks • Studies towards an ecology of complex systems • Complex systems approaches for the study of dynamic human-environment interactions • Using knowledge of nonlinear phenomena to better guide policy development for adaptation strategies and mitigation to environmental change • New tools and methods for studying ecological complexity